The carrier envelope (CE) phase of a femtosecond laser was stabilized. The laser produces an ultra stable comb of frequency spanning the visible region and basically is an optical frequency synthesizer and ready for the frequency domain applications. In this context, the CW stability of the Ti:sapphire laser is discussed to provide a procedure for the femtosecond laser adjustments. In addition, the pulse trains emitted by the femtosecond laser are described analytically to provide a theoretical basis for carrier envelope phase stabilization. An f to 2f interferometer was used to detect the carrier envelope offset frequency, and a fast photo diode was employed to measure the repetition rate. Two similar designed phase lock loops are used to stabilize both the carrier envelope offset frequency and the repetition rate to the respective reference frequencies. The stability reaches 100mHz for the carrier envelope offset frequency and 10mHz for the repetition rate for a period of up to an hour. Doppler free iodine saturation spectroscopy was set up to provide a precise frequency reference to which a CW dye laser can be locked on. The near future goal is to accurately measure this frequency stabilized dye laser with the optical frequency synthesizer.

Fast neural oscillations known as beta (12-30Hz) and gamma (30-100Hz) rhythms are recorded across several brain areas of various species. They have been linked to diverse functions like perception, attention, cognition, or interareal brain communication. The majority of the tasks performed by the brain involves communication between brain areas. To efficiently perform communication, mathematical models of brain activity require representing neural oscillations as sustained and coherent rhythms. However, some recordings show that fast oscillations are not sustained or coherent. Rather they are noisy and appear as short and random epochs of sustained activity called bursts. Therefore, modeling such noisy oscillations and investigating their ability to show interareal coherence and phase synchronization are important questions that need to be addressed. In this thesis, we propose theoretical models of noisy oscillations in the gamma and beta bands with the same properties as those observed in in \textit{vivo}. Such models should exhibit dynamic and statistical features of the data and support dynamic phase synchronization. We consider networks composed of excitatory and inhibitory populations. Noise is the result of the finite size effect of the system or the synaptic inputs. The associated dynamics of the Local Field Potentials (LFPs) are modeled as linear equations, sustained by additive and/or multiplicative noises. Such oscillatory LFPs are also known as noise-induced or quasi-cycles oscillations. The LFPs are better described using the envelope-phase representation. In this framework, a burst is defined as an epoch during which the envelope magnitude exceeds a given threshold. Fortunately, to the lowest order, the envelope dynamics are uncoupled from the phase dynamics for both additive and multiplicative noises. For additive noise, we derive the mean burst duration via a mean first passage time approach and uncover an optimal range of parameters for healthy rhythms. Multiplicative noise is shown theoretically to further synchronize neural activities and better explain pathologies with an excess of neural synchronization. We used the stochastic averaging method (SAM) as a theoretical tool to derive the envelope-phase equations. The SAM is extended to extract the envelope-phase equations of two coupled brain areas. The goal is to tackle the question of phase synchronization of noise-induced oscillations with application to interareal brain communication. The results show that noise and propagation delay are essential ingredients for dynamic phase synchronization of quasi-cycles. This suggests that the noisy oscillations recorded in \textit{vivo} and modeled here as quasi-cycles are good candidates for such neural communication. We further extend the use of the SAM to describe several coupled networks subject to white and colored noises across the Hopf bifurcation ie in both quasi-cycle and limit cycle regimes. This allows the description of multiple brain areas in the envelope-phase framework. The SAM constitutes an appropriate and flexible theoretical tool to describe a large class of stochastic oscillatory phenomena through the envelope-phase framework.

Die vorliegende Arbeit ist der Verbesserung der Carrier-Envelope Phasenstabilisierung von ultrakurzen Laserimpulsen gewidmet. Zur Realisierung von Fortschritten auf diesem Gebiet werden die grundlegenden Rauschquellen identifiziert, die das erzielbare Restphasenrauschen limitieren, und geeignete Maßnahmen zu deren Verringerung vorgeschlagen. Es wird gezeigt, dass sowohl die Messung der Carrier-Envelope Phase (CEP) als auch deren Kontrolle durch verschiedene Rauschbeiträge beeinträchtigt wird. Der Detektionsprozess ist dabei einerseits durch technische Rauschquellen beeinflusst, die vor allem in den verwendeten nichtlinearen Interferometern auftreten. Andererseits repräsentiert das Detektionsrauschen während der elektro-optischen Wandlung eine fundamentale Limitierung, da das optische Schrotrauschen sowie das Rauschen des Lichtdetektors die Messung der CEP unausweichlich beeinträchtigen. Es wird demonstriert, wie solche Beschränkungen durch geeignete Wahl der Interferometertopologie, bzw. durch Optimierung des spektralen Verbreiterungsmechanismus verringert werden können. Experimentell gelingt es dadurch den Signal-Rauschabstand der Phasenmessung um 20 Dezibel zu steigern. Hinsichtlich der CEP Kontrolle von Oszillatoren wird in dieser Arbeit ein neuartiges Doppelstabilisierungskonzept vorgestellt, welches eine feed-forward Stabilisierung, die auf einem akustooptischen Frequenzschieber beruht, mit einer klassischen Feedback Regelung kombinert. Mit diesem Konzept gelingt eine Reduzierung des Phasenrestrauschen auf beispiellose 20 Milliradian. Darüber hinaus werden weitere neue Stabilisierungskonzepte vorgestellt, die ohne Feedback zu dem Laseroszillator auskommen. Bei einem dieser Konzepte, handelt es sich um eine gepulste feed-forward Stabilisierung, die speziell für das Zusammenwirken mit einer Verstärkerstufe konzipiert ist. Erste experimentelle Ergebnisse zeigen, dass Phasenrestrauschen von weniger als 100 Milliradian auch für Verstärkersysteme erreichbar sind. / The present thesis is dedicated to improvements of the carrier-envelope phase stabilization of ultrashort laser pulses. In order to realize such improvements, the fundamental noise sources are identified, and suitable measures for their reduction are proposed. It is shown that both, the measurement of the carrier-envelope phase (CEP) as well as its control are corrupted by different noise contributions. On the one hand, the detection process is influenced by technical noise sources, which arise especially in the used nonlinear interferometers. On the other hand, the detection noise in the electro-optic conversion represents a fundamental limitation, since the optical shot noise as well as the noise induced by the light detector inevitably influence the measurement of the CEP. It is demonstrated how such limitations can be minimized by a suitable choice of the interferometer topology and by an optimization of the spectral broadening process in a micro-structured fiber. This way an enormous improvement of the signal-to-noise ratio by 20 dB is obtained experimentally, which significantly reduces the limitation of detection noise. For controlling the CEP of mode-locked oscillators, a novel double stabilization scheme is introduced in this thesis, which combines a feed-forward stabilization based on an acousto-optic frequency shifter, with a classical feedback loop. This method enables a reduction of the residual phase jitter to an unprecedented value of 20 milliradian. Beyond that, several further concepts are introduced that are capable of stabilizing the CEP without any feedback to the laser oscillator. One of these concepts, represents a pulsed feed-forward stabilization, which is specifically designed for the use in combination with a subsequent amplification stage. First experimental results indicate that residual phase jitters of less than 100 milliradian are within reach also for amplified laser systems.

There is increasing interest in the generation of very short laser pulses, even down to attosecond (10-18 s) durations. Laser systems with femtosecond pulse durations are needed for these applications. For many of these applications, positioning of the maximum electric field within the pulse envelope can affect the outcome. The peak of the electric field relative to the peak of the pulse is called the Carrier Envelope Phase (CEP). Controlling the position of the electric field becomes more important when pulse duration approaches single-cycle. This thesis focuses on the stabilization of a quasi-single-cycle laser facility. Improvements to this already-established laser facility, HERACLES (High Energy, Repetition rate Adjustable, Carrier-Locked-to-Envelope System) described in this thesis include a stabilized pump line and the improvement in CEP stabilization electronics. HERACLES is built upon an Optical Parametric Chirped Pulse Amplification (OPCPA) architecture. This architecture uses Optical Parametric Amplification (OPA) as the gain material to increase the output energy of the system. OPA relies on a nonlinear process to generate high gain (106 ) with ultra-wide bandwidth. Instabilities in the OPA driving pump energy can create dynamically fluctuations in the final OPCPA output energy. To reduce these fluctuations two key upgrades were implemented on the pump beam. Both were major improvements in the stability. Firstly, an improved regenerative amplifier design reduced beam pointing fluctuations. Secondly, the addition of a pump monitoring system with feedback-control eliminated long-term power drifts. Both enhanced the OPA pulse-to-pulse and long-term stability. iv To improve the stability in measuring CEP drifts, modification of the feedback electronics was needed. The modification consisted of integrating noise reduction electronics. This novel noise reducer uses a similar process to a super-heterodyne receiver. The noise reducer resulted in 60 dB reduction of out-of-band noise. This led to increased signal quality with cleaner amplification of weaker signals. The enhanced signal quality led to more reliable long-term locking. The synthetically increased signal-to-noise ratio allows locking of the CEP frequency below the typically requirements. This integration allows relaxed constraints on the laser systems. The optics and electronics of a high-power, quasi-single cycle laser facility were improved. This thesis included the stabilization of the pump line and the stabilization of the CEP. This work allows for new long-duration experiments.

Doctor of Philosophy / Department of Physics / Zenghu Chang / In this research, the carrier-envelope phase (CE phase) evolution of the pulse train from a Kerr-lens mode-locked chirped-mirror dispersion compensated Ti:Sapphire laser oscillator was stabilized. The offset frequency corresponding to the rate of change of the CE phase was obtained by spectrally broadening the oscillator pulses in a photonic crystal fiber and interfering the f and 2f components. An offset frequency linewidth of 100 mHz was obtained and could be locked over several hours. The effect of path length drift in the interferometer used for CE phase stabilization of the laser oscillator was investigated. By stabilizing the path length drift, the interferometer noise was reduced by several orders of magnitude. The CE phase drift through a grating-based chirped-pulse multi-pass amplifier was investigated. Varying the grating separation by 1μm in the stretcher was found to cause a shift of 3.7 +/- 1.2 rad of the CE phase. The CE phase could be stabilized to within 160 mrad rms error by feedback controlling the grating separation. By locking the path length in the f-to-2f interferometer used to stabilize the CE phase of the oscillator pulses, the fast (>3 Hz) CE phase drift of the amplified laser pulses was reduced from 79 to 48 mrad. It was also found that the CE phase could be shifted and set to any value within a 2π range by changing the grating separation. Also, the CE phase could be continuously modulated within a 2π range while maintaining a relative phase error of 171 mrad. The CE phase shift of a grating-based compressor was found to be stabilized to 230 mrad rms. The effect of laser power fluctuation on the CE phase measurement was also investigated. It was found that a 1% fluctuation of the laser energy caused a 160 mrad error in the CE phase measurement. A two-step model is proposed to explain the phase-energy coupling in the CE phase measurement. The model explains the experimentally observed dependence of the group delay between the f and 2f pulses on the laser energy. Few-cycle pulses were CE phase stabilized to 134 mrad rms and were used to perform above-threshold ionization and high harmonic generation.

It is well known that the optical properties of multi-level atomic and molecular system can be controlled and manipulated efficiently using quantum coherence and interference, which has led to many new effects in quantum optics for e.g. lasing action without population inversion, ultraslow light, high resolution nonlinear spectroscopy etc. Recent experimental and theoretical studies have also provided support for the hypothesis that biological systems uses quantum coherence. Nearly perfect excitation energy transfer in photosynthesis is an excellent example of this. In this dissertation we studied quantum coherence and interference effects in the transient and the continuous-wave regimes. This study led to (i) the first experimental demonstration of carrier-envelope phase effects on bound-bound atomic excitation in multi-cycle regime (~15 cycles), (ii) a unique possibility for standoff detection of trace gases using their rotational and vibrational spectroscopic signals and from herein called Coherent Raman Umklappscattering, (iii) several possibilities for frequency up-conversion and generation of short-wavelength radiation using quantum coherence (iv) the measurement of spontaneous emission noise intensity in Yoked-superfluorescence scheme. Applications of the obtained results are development of XUV (X-Ray) lasers, con- trolled superfluorescent (superradiant) emission, carrier-envelope phase effects, coherent Raman scattering in the backward direction, enhancement of efficiency for generating radiation in XUV and X-Ray regime using quantum coherence with and without population inversion and to extend XUV and X-Ray lasing to ~4.023 nm in Helium-like carbon.

In this thesis we present the realization of a source of 1.5-cycle carrier-envelope phase stable laser pulses in the mid-infrared spectral region. We used ytterbium laser system generating 1 µm pulses as a pump of setup, where the beam is split into several parts and interact in nonlinear optical media. 2 µJ pulses with duration 18 fs at 50 kHz repe- tition rate are produced. By spectral broadening in crystal GGG, 9,9 fs pulses can be achieved. The mid-IR pulses was characterized by third harmonics generation frequency resolved optical gating in the interferometric configuration. Fourier filtering of the mea- sured interferogram allows for the complete reconstruction of amplitude and phase of the ultrashort pulses generated by our setup. The pulses will in future serve for experimental investigation of ultrafast strong-field phenomena in solids. 1

Master of Science / Department of Physics / Brett D. Esry / The two-state field-aligned (1-D) model has been employed to investigate the dissociation dynamics of a hydrogen molecular ion and its isotopes under the Born-Oppenheimer approximation without rotation. The emphasis of this work was on the role of mass during the dynamical dissociation processes and on the laser-induced branching ratios between different photon pathways. Firstly, we have found that scaling the pulse duration of the laser pulse, applied to H[subscript]2+ and D[subscript]2+ , by the square root of the mass ratio of these isotopes will produce similar structure in the nuclear kinetic energy release (KER) spectra. In fact, the similarity of the spectra is enhanced by including some averaging that is necessary for comparison with experiment. For this to occur, the same broad initial vibrational distribution and a short pulse are preferred. Using this scaling idea, it is possible to produce effectively shorter laser pulses by studying heavier isotopes, like D[subscript]2+. Secondly, we have demonstrated analytically and numerically that there is a carrier-envelope phase effect in the total dissociation probability (TDP) of H[subscript]2+, and this effect grows with nuclear mass. We further show that under the same laser conditions, the CEP effect in the asymmetry between breakup channels decreases with mass. Our analytic expressions enhance the idea that CEP effects can be understood as an interference between different n-photon processes. Thirdly, the trends in the dissociation dynamics of H[subscript]2+ and D[subscript]2+ in a 800nm ultra short intense laser field were demonstrated by studying the dissociation branching ratios of multiphoton processes as a function of the laser peak intensity (from 8[times]10[superscript]9 to 10[superscript]14 W/cm[superscript]2) or pulse length (5fs-7.5fs). Based on the two-state approximation, an energy-analysis method (EAM) was employed to separate multiphoton processes. The results show that the one-photon dissociation process dominates over all other photon processes under all the laser conditions applied in the calculations and that the zero-photon process contributes to a surprisingly large fraction of the total dissociation. Two- and three- photon dissociation are weaker processes, but become more and more important as the laser peak intensity and pulse length increases. A two-state Floquet method was used to check the accuracy of the EAM, and good agreement between the two methods was found, demonstrating the reliability of the EAM. In comparison with H[subscript]2+, D[subscript]2+ displays stronger two and three photon branching ratios (above-threshold dissociation - ATD), which can be attributed to the late arrival of D[subscript]2+ to the critical distance for ATD to occur due to its heavier mass. Therefore, this "mass" effect can be used to steer the molecular dissociation pathways.

Doctor of Philosophy / Department of Physics / Brett D. Esry / The nuclear rotational period of the simplest molecule H[subscript]2[superscript]+ is about 550 fs, which is more than 35 times longer than its vibrational period of 15 fs. The rotational time scale is also much longer than widely available ultra short laser pulses which have 10 fs or less duration. The large difference in rotational period and ultra short laser pulse duration raises questions about the importance of nuclear rotation in theoretical studies of H[subscript]2[superscript]+ dissociation by these pulses. In most studies, reduced-dimensionality calculations are performed by freezing the molecular axis in one direction, referred to as the aligned model. We have systematically compared the aligned model with our full-dimensionality results for total dissociation probability and field-free dynamics of the dissociating fragments. The agreement between the two is only qualitative even for ultra short 10 fs pulses. Post-pulse dynamics of the bound wave function show rotational revivals. Significant alignment of H[subscript]2[superscript]+ occurs at these revivals. Our theoretical formulation to solve the time-dependent Schrodinger equation is an important step forward to make quantitative comparison between theory and experiment. We accurately calculate observables such as kinetic energy, angular, and momentum distributions. Reduced-dimensionality calculations cannot predict momentum distributions. Our theoretical approach presents the first momentum distribution of H[subscript]2[superscript]+ dissociation by few cycle laser pulses. These observables can be directly compared to the experiment. After taking into account averaging steps over the experimental conditions, we find remarkable agreement between the theory and experiment. Thus, our theoretical formulation can make predictions. In H[subscript]2[superscript]+ dissociation by pulses less than 10 fs, an asymmetry in the momentum distribution occurs by the interference of different pathways contributing to the same energy. The asymmetry, however, becomes negligible after averaging over experimental conditions. In a proposed pump-probe scheme, we predict an order of magnitude enhancement in the asymmetry and are optimistic that it can be observed.

Doctor of Philosophy / Department of Physics / Zenghu Chang / The first part of this thesis describes our novel design, test, and application of our X-ray streak camera to the pulse duration measurement of soft X-rays. We demonstrated a significant improvement in the resolution of the x-ray streak camera by reducing the electron beam size in the deflection plates. This was accomplished by adding a slit in front of the focusing lens and the deflection plates. The temporal resolution reached 280 fs when the slit width was 5 μm. The camera was operated in an accumulative mode and tested by using a 25 fs laser with 2 kHz repetition rate and 1-2% RMS pulse energy stability. We conclude that deflection aberrations, which limit the resolution of the camera, can be appreciably reduced by eliminating the wide-angle electrons. We also employed the same streak camera to demonstrate that it is capable of measuring the pulse duration of X-rays. We measured the pulse duration of X-rays emitted from Ni-like Ag and Cd grazing-incidence laser to be ~5ps. The measured value agrees with the prediction made by the model and the measurement made by changing the delay as a function of the pulse duration. The streak camera was also tested with various sources of X-ray such as high harmonics generation of soft x-rays from an argon atom using a high power Ti:sapphire laser source of KLS. The result of the measurement manifests its capability for serving as a detector in the study of ultrafast dynamics in the field of physics, chemistry, biology and medical sciences. The second part of this thesis describes our design of a spectrometer to study the effect of the Carrier envelope (CE) phase on polarization gated extreme-ultraviolet (XUV) super-continuum generation. Because the challenge of making single shot experiment possible is to generate a sufficient number of photons, our setup has been built to allow generation of high order harmonics at the maximum phase matched pressure. This is the first time to our knowledge that phase matching in the polarization gating process has been studied so far. We measured the maximum phase matching pressure to be ~ 55 Torr which is the pressure above which quadratic increase in intensity of the high harmonics spectrum ceases to appear. At this pressure the number of photons per laser shot was 104 which is sufficient for measuring the single shot XUV spectrum in the range 34 to 45 eV. The spectral profile was a super-continuum for some shots and discrete high harmonics for other shots. It is believed that the shot to shot variation of the spectra is due to the changes of the carrier envelope phase of the few-cycle laser pulses used for the polarization gating. An improved CE phase stabilization system in KLS further eliminated the statistical noise in our observation by allowing us to integrate data over several laser cycles for each CE phase value. The effect of CE phase on a polarization gated XUV spectrum was tested by changing the CE phase with two different methods. In the first method, the CE phase was changed by changing the thickness of fused silica plates on the beam path, and the result shows the shift in the spectral peak of the XUV when the gate width approached less than one optical cycle. As gate width was made less than half the optical cycle, the spectrum was observed with continuum harmonics separated by π radians. We believe that the presence of continuum and discrete harmonics spectra in the observation is due to single and double attosecond pulses generated in the polarization gating. In the second method the carrier-envelope phase of pulses from a grating-based chirped pulse amplification laser was varied smoothly to cover a 2π range by controlling the grating separation. The phase is measured simultaneously by an f-to-2f setup and by the variation of XUV spectra from polarization gated high harmonic generation. A very good similarity between the effect of single and double slits in Yong’s experiment and that of CE phase on the XUV spectrum in the polarization gating experiment has been found, giving better agreement with the theory. The effect of optical properties such as the Gouy phase shift on the polarization gated spectrum has also been studied in the course of investigating the best experimental optimizations to generate the most CE phase sensitive XUV spectrum with less statistical noise. This is the first time to our knowledge experimental study of the effect of the Gouy phase shift on a polarization gated XUV spectrum has been made.